The present invention relates to a new, novel, and distinct variety of plum tree ‘Prunus salicina’ and which has been denominated varietally as ‘Constanza’ and more specifically to a plum tree which produces what are considered to be exceptionally high quality, black plums which are mature for harvesting, and shipping about March 20 to April 10 under the ecological conditions existing in the Maipo Valley of Santiago, Chile.